Modeling Security-Check Queues

• 成果类型: Article
• 署名作者: Zhang, Zhe George; Luh, Hsing Paul; Wang, Chia-Hung
• 署名单位: Lanzhou University; Simon Fraser University; Western Washington University; National Chengchi University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1110.1399
• 发表日期: 2011
• 页码: 1979-1995
• 关键词: security inspection level; service capacity; two-stage queue; renewal process approximation; Coxian distribution; quasi-birth-and-death process

摘要

Motivated by the waiting lines between the U.S.-Canadian border crossings, we investigate a security-check system with both security and customer service goals. In such a system, every customer has to be inspected by the first-stage inspector, but only a proportion of customers need to go through the second stage for further inspection. This further inspection proportion, affecting both security screening and the system congestion, becomes a key decision variable for the security-check system. Using a stylized two-stage queueing model, we established the convexity of the expected waiting cost function. With such a property, the optimal further inspection proportion can be determined to achieve the balance of the two goals and the service capacities can be classified into security-favorable, security-unfavorable, or security-infeasible categories. A specific capacity category implies if the security and customer service goals are consistent or in conflict. In addition, we have verified that the properties discovered in the stylized model also hold approximately in a more general multiserver setting. Numerical results are presented to demonstrate the accuracy and robustness of the approximations and the practical value of the model.